In this work we study the energy transport in a one-dimensional system composed of two dissimilar Frenkel-Kontorova lattices connected by a time-modulated coupling and in contact with two heat reservoirs operating at different temperature by means of molecular dynamics simulations. There is a value of the driving frequency at which the heat flux takes its maximum value, a phenomenon termed as thermal resonance. Structural modifications in the lattice strongly alter the way in which the external driving interacts with the phonon bands. The overlap of the latter in the harmonic regime of the model determine the frequency range wherein resonance emerges. Parameter dependencies by which the incoming heat flux can be directed to either of the heat reservoirs are examined as well. Our results may be conductive to further developments in designing thermal devices.
Heat conduction through the Frenkel-Kontorova (FK) lattices is numerically investigated in the presence of a deformable substrate potential. It is found that the deformation of the substrate potential has a strong influence on heat conduction. The thermal conductivity as a function of the shape parameter is nonmonotonic. The deformation can enhance thermal conductivity greatly and there exists an optimal deformable value at which thermal conductivity takes its maximum. Remarkably, we also find that the deformation can facilitate the appearance of the negative differential thermal resistance (N…
The Frenkel Kontorova (FK) model is known to exhibit the so called Aubry's transition which is a jamming or frictional transition at zero temperature. Recently we found similar transition at zero and finite temperatures in a super-conducting Josephson junction array (JJA) on a square lattice under external magnetic field. In the present paper we discuss how these problems are related.
We propose a new but simpler explanation of the phases of a Frenkel-Kontorova chain of atoms, and we demonstrate it by examples. Combined with this, we present a criticism of the theory of so-called commensurate and incommensurate states, especially for finite chains. We reject the putative observation of an Aubry-phase transition in a finite chain.
A 1D model of interacting particles moving over a periodic substrate and in a position dependent temperature profile is considered. When the substrate and the temperature profile are spatially asymmetric a center-of-mass velocity develops, corresponding to a directed transport of the chain. This autonomous system can thus transform heath currents into motion. The model parameters can be tuned such that the particles exhibit a crossover from an ordered configuration on the substrate to a disordered one, the maximal motor effect being reached in such a disordered phase. In this case the manybody…
Through multiscale analysis of the adjoint Fokker-Planck equation, strict bounds are derived for the center of mass diffusivity of an overdamped harmonic chain in a periodic potential, often known as the discrete Frenkel-Kontorova model. Significantly, it is shown that the free energy barrier is a lower bound to the true finite temperature migration barrier for this general and popular system. Numerical simulation confirms the analysis, whilst effective migration potentials implied by the bounds are employed to give a surprisingly accurate prediction of the non-linear response.
In this paper, the one-dimensional incommensurate quantum Frenkel-Kontorova model is investigate by a density-matrix renormalization group algorithm. Special attention is given to the entanglement and the ground state energy. The energy gap between the ground state and the first excited is also calculated. From all the numerical results, we have observed an obvious property changes from the pinned state to the sliding one as the quantum fluctuation is increased. But no expected quantum critical point can be justified by the present data.
In this paper, we have studied the one-dimensional commensurate quantum Frenkel-Kontorova model by a density-matrix renormalization group (DMRG) algorithm. The focus has been on its properties of the entanglement, the coordinate correlation, the ground state energy and the energy gap between the ground state and the first excited one. It is demonstrated that a quantum phase transition (QPT) between the pinned and the sliding phases takes place as the quantum fluctuation, measured by an effective Planck constant $\tilde\hbar$, increases to a threshold value $\tilde \hbar_c$.
Simple models for friction are typically one-dimensional, but real interfaces are two-dimensional. We investigate the effects of the second dimension on static and dynamic friction by using the Frenkel-Kontorova (FK) model. We study the two most straightforward extensions of the FK model to two dimensions and simulate both the static and dynamic properties. We show that the behavior of the static friction is robust and remains similar in two dimensions for physically reasonable parameter values. The dynamic friction, however, is strongly influenced by the second dimension and the accompanying …
Problems of heat transport are ubiquitous to various technologies such as power generation, cooling, electronics, and thermoelectrics. Within this context it is natural that external heat flux control on nanoscale devices became an appealing strategy that has been explored in recent years. In this work we study the thermal resonance phenomenon, i.e., the maximum heat flux obtained by means of an external periodic driving, of a one-dimensional system composed of two dissimilar Frenkel-Kontorva lattices with both nearest-neighbor (NN) and next-nearest-neighbor (NNN) interactions connected by tim…
Dynamical phase diagram of the dc-driven underdamped Frenkel-Kontorova chain
对欠阻尼极限下的广义Frenkel-Kontorova模型进行了分子动力学模拟，研究了原子在直流外力作用下从锁定态到运行态的多步动力学相变.我们表明，最近报道的过渡层次[Braun等人，Phys. Rev. Lett. 78，1295（1997）]强烈地依赖于摩擦常数的值。一个简单的唯象解释的摩擦依赖性的各种临界力分离中间制度。
We analyze the relationship between the lowest energy configurations of an infinite harmonic chain of particles in a periodic potential and the evolution of characteristics in a periodically-forced inviscid Burgers equation. The shock discontinuities in the the Burgers evolution arise from thermodynamical considerations and play an important role as they separate out flows related to lowest energy configurations from those associated with higher energies. We study in detail the exactly solvable case of an external potential consisting of parabolic segments, and calculate analytically the lowes…
Energy transport control in low dimensional nano-scale systems has attracted much attention in recent years. In this paper, we investigate the energy transport properties of Frenkel-Kontorova lattice subject to a periodic driving force, in particular, the resonance behavior of the energy current by varying the external driving frequency. It is discovered that in certain parameter ranges, multiple resonance peaks, instead of a single resonance, emerge. By comparing the nonlinear lattice model with a harmonic chain, we unravel the underlying physical mechanism for such resonance phenomenon. Othe…
